Back to Exercise: Find conjugates and quotients of complex numbers

Exercises: Find Conjugates and Quotients of Complex Numbers

Show your work. Write all answers in standard form $a + bi$ (or as simplified real numbers where appropriate).

Grade 9·19 problems·~35 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-a-3

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Warm-Up: Review What You Know

What is the result of $(3 + 4i)(3 - 4i)$ ?

$9 - 16i^2$

$25$

$0$

$9 + 16 = 25$

In the division technique $\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ , what principle is being applied?

Cross-multiplication

Multiplying by 1 in the form $\frac{\sqrt{2}}{\sqrt{2}}$ to rationalize the denominator

Taking the reciprocal

Canceling common factors

Use the Pythagorean theorem: in a right triangle with legs $3$ and $4$ , the hypotenuse length is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . Enter a number.

Fluency Practice

What is the conjugate of $-1 - 2i$ ?

$1 + 2i$

$-1 + 2i$

$1 - 2i$

$-1 - 2i$

Compute $|3 + 4i|$ (the modulus). Enter the numerical value.

Compute $|1 + i|$ . Enter the exact value (simplified radical form or decimal).

Compute $\dfrac{2 + 3i}{1 - 2i}$ .

$2 + 3i$

$\dfrac{2 + 3i}{5}$

$-\dfrac{4}{5} + \dfrac{7}{5}i$

$-4 + 7i$

Compute $\dfrac{5 + i}{2 + 3i}$ . What is the real part of the result (as a fraction)? Enter a fraction or decimal.

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